A Planar Focusing Antenna Design With the Quasi-Conformal Mapping

Abstract

Abstract-We propose a planar focusing antenna design, which has the same performance as its parabolic counterparts and can be realized using PEC-backed gradient index dielectrics. In this design, quasi-conformal transformation optics is first utilized to transform a parabolic surface into a planar one, then the anisotropy factor of the resultant material is minimized, and the material is approximately treated as isotropic. Examples with realizable material parameters are given, and the simulation results validate the design. The proposed method could be used to design planar focusing antennas with high directivity and similar devices. The idea can also be applied to new device designs in optics engineering.

A versatile smart transformation optics device with auxetic elasto-electromagnetic metamaterials

“…To implement the intricate gradient permittivity and/or permeability distributions designed by the TO theory, many researchers employed the novel concept of artificially structured metamaterials, which consist of deeply subwavelength unit cells coupling with electromagnetic waves collectively as an effective medium. From the first introduction of TO theory 1 , various TO applications have been suggested using metamaterials, such as cloaking 1 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 , arbitrary light guiding 18 19 , extreme imaging lenses 20 21 22 23 , and other interesting approaches to manipulating light 24 25 . Amongst those applications, invisibility cloaks 1 2 contributed most significantly to the continued public curiosity and led to the expansion of related research fields 26 27 .…”

Transformation electromagnetics and its applications (Invited paper)

“…Due to the complexity of the resulting materials, only finite‐element‐method (FEM) based simulation results were given and they clearly showed that the planar antenna has the same performances as the parabolic reflector. In 2011, our group optimized the transformation function and utilized quasi‐conformal mapping instead of the general transformation, which means a big step forward to the practical usage of the proposed antenna [54, 55]. Similar results are independently given by Tang et al [83].…”

“…the minimum for this functional occurs at the quasi‐conformal mapping [66], which can be numerically calculated using grid generation techniques or by solving Laplace's equation [67, 70]. The readers are referred to our previous work for the detailed process [44, 54, 55]. One should note that quasi‐conformal mapping is not a rigorous solution in the TO frame, and the distortion between virtual and physical spaces can not be big, otherwise, large discrepancies occur.…”

“…Several applications using the above‐mentioned transformations are detailed in the third part of the review. They include a radar illusion device [50], a microwave bend structure [51, 52], a flattened Luneburg lens [53], a planar focusing lens antenna [54, 55], and a three‐dimensional (3D) broadband carpet cloak [56, 57]. Finally, we give the conclusion.…”

Illusion optics: Optically transforming the nature and the location of electromagnetic emissions

“…For microwave antenna applications, focusing lens antennas have been theoretically designed. 12,13 The performances of an omnidirectional retroreflector 14 based on the transmutation of singularities and a Luneberg lens 15 have been experimentally demonstrated. Techniques of source transformation [16][17][18][19][20][21][22][23] have offered new opportunities for the design of active devices with source distribution included in the transformed space.…”